Well lets try to resurrect a dead forum for a few questions.
1. Can you climb along the ground at full climb speed or do you have to be climbing to use the climb speed. What is defined as climbing vs not. When is something steep enough to transition between walking and climbing?
2. The rules for climb speed state the following "The creature must make a Climb check to climb any wall or slope with a DC higher than 0, but it can always choose to take 10, even if rushed or threatened while climbing. If a creature with a climb speed chooses an accelerated climb (see above), it moves at double its climb speed (or at its land speed, whichever is slower) and makes a single Climb check at a –5 penalty."
so if you had an eidolon with a base speed of 20' and a climb of 40' then either you slow down when using accelerated climbing or your climb speed can never exceed your base speed. But if you can never exceed your base with climb then why does the ediolon climb evolution specifically allow you to go over your base speed by taking it more than once?